|
Several examples with detailed solutions and exercises with answers on fractions addition, are presented.
a / b is used here to denote the fraction of a over b. a is called the numerator and b is called the denominator and must be non zero.
Examples of fractions: 2 / 3 , -3 / 4 .
NOTE: 2 / 0 is undefined since division by zero is undefined in mathematics.
A calculator to add fractions is included in this website. You may use it to check your answers.
How to add fractions?
1. Add fractions with equal denominator
Example 1: Add and simplfy.
2 / 3 + 4 / 3
Solution to Example 1
To add fractions with the same denominator, you only the numerators and simplify if possible
2 / 3 + 4 / 3 = (2 + 4) / 3 = 6 / 3 = 2
Example 2: Add, simplfy and express the final answer as a fraction.
12 / 14 + 34 / 14
Solution to Example 2
Add the numerators
12 / 14 + 34 / 14 = (12 + 34) / 14 = 46 / 14 = 23 / 7
2. Add fractions with non equal denominators
Example 3: Add, simplfy and express the final answer as a fraction.
2 / 9 + 4 / 6
Solution to Example 3
We first need to find the lowest common multiple (LCM) of the denominators 9 and 6 by factoring into prime factors.
9 = 3 * 3
6 = 2 * 3
LCM = 3 * 3 * 2 = 18
We next convert the two given fractions so the they have common denominator equal to the LCM = 18. The denominator of the fraction 2 / 9 is 9 and we need to multiply numerator and denominator by 2 in order to change the denomiantor to 18
2 / 9 = (2 * 2) / (2 * 9) = 4 / 18
The denominator of the fraction 4 / 6 is 6 and we need to multiply numerator and denominator by 3 in order to change the denomiantor to 18
4 / 6 = (3 * 4)/(3 * 6) = 12 / 18
Now that we have converted the two fractions so that they have common denominator, we can easily add as follows
2 / 9 + 4 / 6 = 4 / 18 + 12 / 18 = (4 + 12) / 18 = 16 / 18 = 8 / 9
Example 4: Add, simplfy and express the final answer as a fraction and as a mixed number.
23 / 15 + 27 / 55
Solution to Example 3
Find the LCM of the denominators 15 and 55
15 = 3 * 5
55 = 5 * 11
LCM = 3 * 5 * 11 = 165
We convert the given fractions so the they have common denominator equal to the LCM = 165. The denominator of the fraction 23 / 15 is 15 and both numerator and denominator need to be multiplied by 11 in order to change the denomiantor to 165
23 / 15 = (11 * 23) / (11 * 15) = 253 / 165
The second fraction 27 / 55 is converted to one with the denominator equal to 165 by multiplying numerator and denominator by 3 in order to change the denomiantor to 165
27 / 55 = (3 * 27) / (3 * 55) = 81 / 165
We now add the fractions
23 / 15 + 27 / 55 = 253 / 165 + 81 / 165
= (253 + 81) / 165 = 334 / 165
= 2 4 / 165 (mixed number)
Example 5: Add, simplfy and express the final answer as a fraction.
2 + 1 / 5
Solution to Example 5
We first convert 2 into a fraction
2 = 2 / 1
The common denominator will be 5
2 = 2 / 1 = 10 / 5
We now add
2 + 1 / 5 = 10 / 5 + 1 / 5 = 11 / 5
Exercises: Add, simplify and express the answer as a fraction and as a mixed number.
1. 2 / 3 + 5 / 7
2. 23 / 30 + 33 / 25
3. 5 - 2 / 6
Answers to Above Exercises:.
1. fraction: 29 / 21 mixed number: 1 8/21
2. fraction: 313 / 150 mixed number: 2 13/150
3. fraction: 14 / 3 mixed number: 4 2 / 3
More on fractions
and fraction calculators.
|